{Use of Tech} Cell population The population of a culture of cells after t days is approximated by the function P(t)=1600 / 1 + 7e^−0.02t, for t≥0.
a. Graph the population function.  

Evaluate and simplify y'.

y = (3t²−1 / 3t²+1)^−3

Tangent lines Determine an equation of the line tangent to the graph of y=(x²−1)² / x³−6x−1 at the point (0,−1).

Finding derivatives from a table Find the values of the following derivatives using the table. <IMAGE>

d. d/dx (f(x)³) |x=5

27–76. Calculate the derivative of the following functions.

y = √f(x), where f is differentiable and nonnegative at x.

{Use of Tech} Tangent lines Determine equations of the lines tangent to the graph of y= x√5−x² at the points (1, 2) and (−2,−2). Graph the function and the tangent lines.

9–61. Evaluate and simplify y'.

y = (v / v+1)^4/3

109-112 {Use of Tech} Calculating limits The following limits are the derivatives of a composite function g at a point a.

b. Use the Chain Rule to find each limit. Verify your answer by using a calculator.

$\underset{x\to 2}{\lim }\frac{{(x^2-3)}^5-1}{x-2}$

109-112 {Use of Tech} Calculating limits The following limits are the derivatives of a composite function g at a point a.

b. Use the Chain Rule to find each limit. Verify your answer by using a calculator.

$\underset{x\to 0}{\lim }\frac{\sqrt{4+\sin \left(x\right)}-2}{x}$